WASHINGTON — Rudolph W. Giuliani seemed drunk, and he was making a beeline for the president.

It was election night in 2020, and President Donald J. Trump was seeing his re-election bid slip away, vote by vote. According to video testimony prepared by the House committee investigating the Jan. 6 assault on the Capitol, Mr. Giuliani, the former New York City mayor and personal lawyer for Mr. Trump, was spouting conspiracy theories.

“They’re stealing it from us,” Mr. Giuliani told the president when he found him, according to Jason Miller, one of the president’s top campaign aides, who told the Jan. 6 committee that Mr. Giuliani was “definitely intoxicated” that night. “Where do all the votes come from? We need to go say that we won.”

Several times that night, Mr. Trump’s own family members and closest advisers urged him to reject Mr. Giuliani’s advice. Mr. Miller told him not to “go and declare victory” without a better sense of the numbers. “It’s far too early to be making any proclamation like that,” said Bill Stepien, his campaign manager. Even his daughter Ivanka Trump told him that the results were still being counted.

But in the end, Mr. Giuliani was the only one that night who told the president what he wanted to hear.

Mr. Giuliani’s rantings about stolen ballots fed into the president’s own conspiracy theories about a rigged election, nursed in public and private since long before the votes were counted. They helped spark a monthslong assault on democracy and — in the committee’s view — led inexorably to the mob that breached the Capitol hoping to stop the certification of Joseph R. Biden Jr. as president.

Mr. Trump told Mr. Miller, Mr. Stepien and the rest that they were being weak and were wrong. During a conversation in the reception area of the White House living quarters, he told them he was going to go in “a different direction.”

Not long after, Mr. Trump did just that, appearing for the cameras at 2:21 a.m. in the East Room in front of a wall of American flags.

He denounced the election in the speech, calling the vote “a fraud on the American public” and an “embarrassment” to the country. “We were getting ready to win this election,” he told his supporters and the television viewers. “Frankly, we did win this election.”

The inside account of the White House that night was assembled by the Jan. 6 committee. During its second public hearing on Monday, the committee played a video that painted a vivid portrait of how Mr. Trump rejected cautions from his closest aides and advisers and went out to declare himself the winner.

Testimony from those closest to the former president effectively documented the formal beginning of Mr. Trump’s insistence that the election was stolen.

Mr. Trump had not been shy about that expectation; weeks before Election Day, he had predicted a “fraud like you’ve never seen.” And even as the votes were being counted, Mr. Trump began delivering that message. But the testimony offered at Monday’s hearing was the linchpin of the argument that the committee is trying to make: that Mr. Trump knew his claims of a fraudulent election were not true and made them anyway.

“That’s the bottom line,” said Representative Bennie Thompson, the Mississippi Democrat who is chairman of the committee. “We had an election Mr. Trump lost, but he refused to accept the results of the democratic process.”

In the weeks to follow election night, Mr. Trump was repeatedly told by top aides that his claims of fraud were baseless.

The committee underscored that fact with long video clips of former Attorney General William P. Barr, who said that beating back the “avalanche” of fraud allegations from the president was “like playing whack-a-mole because something would come out one day and then the next day it would be another issue.” He called the claims of fraud from Mr. Trump and Mr. Giuliani “completely bogus and silly and usually based on complete misinformation.”

But the committee’s depiction of the White House on election night was the day’s most compelling narrative. And the testimony by Trump aides saying they had doubts about Mr. Trump’s claims of fraud was striking, particularly because some of those same aides had expressed support for the president in public, casting doubt on the outcome of the election.

At just after 11:15 p.m., Fox News called Arizona for Mr. Biden, a major blow to Mr. Trump’s campaign. Using interviews with Ivanka Trump, her husband, Jared Kushner, and several of the president’s campaign aides, the committee video captured how the sense of celebration inside the White House residence turned from giddy optimism to grim anxiety.

“Both disappointed with Fox and concerned that maybe our data or our numbers weren’t accurate,” Mr. Miller testified, describing the mood among the president’s supporters.

After the Arizona call, Mr. Trump’s team was livid, according to earlier reporting about the night. Mr. Trump told aides to get Fox News to reverse course somehow. Mr. Miller made a call to a contact at the network. Mr. Kushner reached out to the network’s owner.

“Hey, Rupert,” the president’s son-in-law said into a cellphone as Rupert Murdoch, the head of the network’s corporate parent, took his call.

But soon, there would be another concern for the group of aides who later were referred to as “Team Normal,” according to Mr. Stepien. They received an alarming warning: Mr. Giuliani had had too much to drink and had made his way upstairs to the living quarters, where the president was watching returns.

Several of Mr. Trump’s aides tries to run interference, but Mr. Giuliani, who had been staring at the screens in the campaign war room and insisted that the president had won Michigan, was undeterred.

He demanded to see the president, according to a former aide familiar with the conversation.

Mr. Stepien confronted Mr. Giuliani. How are we winning? he asked him. Mark Meadows, the White House chief of staff, was there as well, and told Mr. Giuliani that he was wrong to say Mr. Trump had won Michigan.

“That’s not true, Rudy!” he said loudly, according to the person familiar with the conversation. (Mr. Meadows would almost immediately go on to publicly and privately embrace the president’s fraud accusations, as documented in text messages discovered by the committee.)

The president’s aides soon failed in their effort to keep Mr. Giuliani away from him. In the video presentation, Mr. Giuliani dismissed his rivals for their attempts to stop him from giving the president his advice.

“I spoke to the president,” he told the committee investigators. “They may have been present. But I talked to the president several times that night.”

Few of the president’s aides went public with their doubts about the president’s chances in the days after the election. In fact, it was the opposite. During a conference call with reporters the day after the election, Mr. Stepien said that he believed Mr. Trump would win Arizona by 30,000 votes when the counting was over.

Mr. Trump had been saying for months that he would win the election, even as polling showed him behind Mr. Biden, in a political climate soured by Mr. Trump’s bumbling and erratic performance during the coronavirus pandemic. But he still started sowing seeds of doubt about the reliability of mail-in ballots, made available more broadly because of the pandemic, much earlier in the year.

Warned weeks before Election Day that those ballots, along with the ones cast through early voting, would be tallied later than the same-day votes cast for Mr. Trump, the president stunned advisers by declaring he would simply go out and say he had won.

“We want all voting to stop,” Mr. Trump said in his remarks early the morning of Nov. 4. “We don’t want them to find any ballots at 4 o’clock in the morning and add them to the list. OK?”

Later that day, Ivanka Trump sent a text to a chain that included Mr. Meadows: “Keep the faith and the fight!” Mr. Trump almost immediately began telling Mr. Giuliani to start gathering what information he could.

By Friday, it was clear from the Trump campaign’s data guru that the numbers simply were not there for him to succeed. The following day, Mr. Stepien, Mr. Miller and other aides were sent by Mr. Kushner to tell Mr. Trump that he had extremely low odds of any success coming from ongoing challenges.

When the men arrived at the White House residence, Mr. Trump was calm, but he was not interested in heeding the warnings. He continued repeating his election conspiracies after Monday’s hearing, issuing a rambling 12-page response with a simple bottom line:

“They cheated!” he wrote.